System Level Numerical Analysis of a Monte Carlo Simulation of the E. Coli Chemotaxis

TL;DR

This paper demonstrates a multiscale computational approach that links microscopic Monte Carlo simulations of E. coli chemotaxis with macroscopic numerical analysis using coarse timesteppers, enabling system-level analysis without explicit macroscopic models.

Contribution

It introduces a system-level numerical analysis framework applying coarse timesteppers to kinetic Monte Carlo simulations of E. coli chemotaxis, bypassing the need for explicit macroscopic equations.

Findings

Successful application of coarse timesteppers to E. coli chemotaxis simulation

Enabled system stability analysis and acceleration of microscopic simulations

Demonstrated multiscale computational methodology for biological systems

Abstract

Over the past few years it has been demonstrated that "coarse timesteppers" establish a link between traditional numerical analysis and microscopic/ stochastic simulation. The underlying assumption of the associated lift-run-restrict-estimate procedure is that macroscopic models exist and close in terms of a few governing moments of microscopically evolving distributions, but they are unavailable in closed form. This leads to a system identification based computational approach that sidesteps the necessity of deriving explicit closures. Two-level codes are constructed; the outer code performs macroscopic, continuum level numerical tasks, while the inner code estimates -through appropriately initialized bursts of microscopic simulation- the quantities required for continuum numerics. Such quantities include residuals, time derivatives, and the action of coarse slow Jacobians. We demonstrate how these coarse timesteppers can be applied to perform equation-free computations of a kinetic Monte Carlo simulation of E. coli chemotaxis. Coarse-grained contraction mappings, system level stability analysis as well as acceleration of the direct simulation, are enabled through this computational multiscale enabling technology.